$J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 4x - 9$ and $ JT = 9x - 34$ Find $CT$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {4x - 9} = {9x - 34}$ Solve for $x$ $ -5x = -25$ $ x = 5$ Substitute $5$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 4({5}) - 9$ $ JT = 9({5}) - 34$ $ CJ = 20 - 9$ $ JT = 45 - 34$ $ CJ = 11$ $ JT = 11$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {11} + {11}$ $ CT = 22$